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Abstract <p>A flat act over a simigroup (as well as a flat module over a ring) is such act <i>A</i> that functor <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(A \otimes - \)</EquationSource> <!--RusMath2570071Pryanichnikov-m1--> </InlineEquation> preserves monomorhpisms. Flat modules over rings, acts over semigroups are modules or acts such that functor <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(A \otimes - \)</EquationSource> <!--RusMath2570071Pryanichnikov-m2--> </InlineEquation> preserves monomorphisms. A unar, that is, a set with only an unary operation can be considered to be an act over a free cycle semigroup. It is shown that a unar is flat iff it is a coproduct of unars, each of which is a line, ray, or cycle.</p>

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Flat Unars

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • A. M. Pryanichnikov

摘要

Abstract

A flat act over a simigroup (as well as a flat module over a ring) is such act A that functor \(A \otimes - \) preserves monomorhpisms. Flat modules over rings, acts over semigroups are modules or acts such that functor \(A \otimes - \) preserves monomorphisms. A unar, that is, a set with only an unary operation can be considered to be an act over a free cycle semigroup. It is shown that a unar is flat iff it is a coproduct of unars, each of which is a line, ray, or cycle.